Investigation into the elliptic curve cryptography

Elliptic curve cryptography (ECC) in TLS, PGP and SSH, which are just three of the main technologies on which the modern web and IT world are based. However, Compared with RSA public key algorithm, ECC is mysterious and not understandable to most. Few literatures introduce how to partition the plaintext into blocks for ECC and how to map the digital codes of block into the points over elliptic curve. For the arithmetic of the points over elliptic curve, the algorithm of multiples of points is the most crucial, how to optimize this algorithm and perform its time complexity analysis are very important. This paper addresses the above works about ECC, and illustrates an example of ECC encryption algorithm implementation.